Related papers: Seniority-zero Linear Canonical Transformation The…
In this work we apply point canonical transformations to solve some classes of nonautonomous nonlinear Schr\"{o}dinger equation namely, those which possess specific cubic and quintic - time and space dependent - nonlinearities. In this way…
The time-dependent Schroedinger equation with time-independent Hamiltonian matrix is a homogeneous linear oscillatory system in canonical form. We investigate whether any classical system that itself is linear, homogeneous, oscillatory and…
Schrieffer-Wolff transformation (SWT) has been extensively used in quantum many-body physics to calculate the low energy effective Hamiltonian. It provides a perturbative method to comprehend the renormalization effects of strong…
Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is a numerical technique for solving strongly coupled QFTs, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is…
It is shown that any two Hamiltonians H(t) and H'(t) of N dimensional quantum systems can be related by means of time-dependent canonical transformations (CT). The dynamical symmetry group of system with Hamiltonian H(t) coincides with the…
We implement the Numerical Unified Transform Method to solve the Nonlinear Schr\"odinger equation on the half-line. For so-called linearizable boundary conditions, the method solves the half-line problems with comparable complexity as the…
Transcorrelated methods provide an efficient way of partially transferring the description of electronic correlations from the ground state wavefunction directly into the underlying Hamiltonian. In particular, Dobrautz et al. [Phys. Rev. B,…
Schr\"odinger's equation serves as a fundamental component in characterizing quantum systems, wherein both quantum state tomography and Hamiltonian learning are instrumental in comprehending and interpreting quantum systems. While numerous…
We introduce a quantum information theory-inspired method to improve the characterization of many-body Hamiltonians on near-term quantum devices. We design a new class of similarity transformations that, when applied as a preprocessing…
The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or…
For almost 75 years, the general solution for the Schr\"odinger equation was assumed to be generated by an exponential or a time-ordered exponential known as the Dyson series. We study the unitarity of a solution in the case of a singular…
The linear canonical transform (LCT) serves as a powerful generalization of the Fourier transform (FT), encapsulating various integral transforms within a unified framework. This versatility has made it a cornerstone in fields such as…
Quantum Monte Carlo methods are powerful numerical tools to accurately solve the Schr\"odinger equation for nuclear systems, a necessary step to describe the structure and reactions of nuclei and nucleonic matter starting from realistic…
We obtain a modified version of the Onsager regression relation for the expectation values of quantum-mechanical operators in pure quantum states of isolated many-body quantum systems. We use the insights gained from this relation to show…
This paper develops practical summation techniques in ZXW calculus to reason about quantum dynamics, such as unitary time evolution. First we give a direct representation of a wide class of sums of linear operators, including arbitrary…
We present the reaction-coordinate polaron-transform (RCPT) framework for generating effective Hamiltonian models to treat nonequilibrium open quantum systems at strong coupling with their surroundings. Our approach, which is based on two…
We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…
Electronic structure simulation is an anticipated application for quantum computers. Due to high-dimensional quantum entanglement in strongly correlated systems, the quantum resources required to perform such simulations are far beyond the…
Linear canonical transforms (LCTs) are of importance in many areas of science and engineering with many applications. Therefore a satisfactory discrete implementation is of considerable interest. Although there are methods that link the…
Solving the electronic Schrodinger equation for strongly correlated ground states is a long-standing challenge. We present quantum algorithms for the variational optimization of wavefunctions correlated by products of unitary operators,…